Prove that the greatest integer function defined by `f(x)= [x], 0 lt x lt 3` is not differentiable at x=1 and x=2.

f(x) {(|x-(1)/(2)|",",0 le x lt 1),(x[x]",",1 le x lt 2):} where [.] denotes the greatest integer function. Show that f(x) is continuous at x=1 but not differentiable at x=1.

Let [.] represent the greatest integer function and f (x)=[tan^2 x] then :

Find all the points of discontinuity of the greatest integer function defined by f(x)= [x], where [x] denotes the greatest integer less than or equal to x.

Prove that the Greatest Integer Function f : R rarr R , given by f(x) = [x] , is neither one - one nor onto , where [x] denotes the greatest integer less than or equal to x.

Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) is

f (x)= {x} and g(x)= [x]. Where { } is a fractional part and [ ] is a greatest integer function. Prove that f(x)+ g(x) is a continuous function at x= 1.

Let f and g be real functions defined by f(x)= 2x + 1 and g(x)= 4x- 7 . For what real numbers x, f(x) lt g(x) ?

The function g(x) = {{:(x+b",",x lt 0),(cos x",",x ge 0):} can be made differentiable at x = 0.